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Data from a GPS scintillation monitor based on 50 Hz measurements recorded at Dirigibile Italia Station (Ny-Alesund, Svalbard), in the frame of the ISACCO project (De Franceschi et al., 2006) are used to investigate possible adoption of an alternative parameter for the estimate of phase fluctuations: i.e., the standard deviation of the phase rate of change Sϕ.
However, the possible existence of higher modes within the whole wavefield, even with rather low amplitudes, might bias the estimate of phase velocities from amplitude ratios (Kurrle et al. 2010).
The estimate of phase for each segment of length n was referenced to the mid point of that segment in time (t), and the estimates were assembled into a sequential time series of Φ t,n).
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A numerical method has been presented for obtaining the estimates of phase velocity and dimensionless frequencies of vibration of transversely isotropic bone using the half-interval method.
The estimates of phase and code ISBs can be accomplished on zero or short baselines, as described in the previous section.
Possible reasons are the following: 1) the phase changes happened in a narrow frequency band around 20 Hz (see the previous section of Discussion) in contrast to the wide band ERP response and 2) effects of AR on C1 and P1 amplitude were too small or too short lived to have a measurable effect on the signal-to-noise ratio and, consequently, on the estimates of phase synchrony.
Once all groups have been processed for all transmit-receive antenna pairs, the phase difference Δ ^ ϕ ( q ), ( q + 1 ) between ϕ q and ϕ q +1 can be obtained from the estimates of phase-rotated channel gains on q0 and q1 as Δ ^ ϕ ( q ), ( q + 1 ) = angle ∑ l, m H ̃ ^ l, m ( q 1 ) H ̃ ^ l, m * ( q 0 ) (26).
For each group q, based on H ̃ ^ l, m ( k ) : k ∈ L ( q, l ), the estimates of phase-rotated channel gains on all tones within the group q denoted by H ̃ ^ l, m ( k ) : k ∈ J q are obtained by interpolation/extrapolation (we use cubic interpolation).
The key aspect of our work is that the phase sparse constraint is applied in each iteration by retaining only phase elements that are larger than thresholding parameter and setting others equal to zero and thus refine the estimate of the phase.
Moreover, by replacing the estimate of the phase and the amplitude of each path in (8) we get (15).
β ^ i, m is the estimate of the phase for i th subcarrier of m th user.
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